So, a couple of things about Rey. One, TLJ just continues the way her character started in TFA. If you watch both closely, you will find that everything she does she picks up from Kylo Ren. Everything she does, he does around her first. And as for her raw power, we got a very good answer for that from Snoke. When Kylo brought Rey before him he said that he’d told Kylo that as he grew stronger his opposite in the light would rise, but Snoke thought it would be Skywalker. So we have a third generation Skywalker who has turned to darkness and to balance that out, his equal in the light has appeared. That is the answer to why things seem to come so easy for her. But while the force seems to come easy for her, she needs a mentor to guide her. Han is dead. Luke refused. Her parents were drunks and are dead. Rey is completely different from Luke. Unlike him who was pretty whiny to start out with, she doesn’t complain much and her life on Jakku taught her the disciple that Yoda tried to teach Luke. But when you look at the duration of Luke’s training, he was with Ben for a few hours in hyperspace. Three years later he could pull a light saber to him and hit targets with incredible accuracy. After he trains with Yoda, we do not have proof that he can lift an X-wing yet, but he flies off with his training incomplete to helps his friends and gets his hand cut off. A year later, with no additional training, he frees Han, turns himself over to the Empire, faces Vader, taps into the raw power of the force (seemingly the dark side from how he was goaded into an emotional response by Vader) and defeats Vader - with no additional formal training than he had the last time they faced.
So, no, the Star Wars universe does not demand formal training to use the force. Anakin could pod-race at 9 using skills normally found in trained Jedi. It was raw talent. Luke always doubted and he had trouble learning. Rey had the discipline of a hard life and the guidance of Kylo Ren (remember that nice lesson he gave her during their lightsaber duel on Starkiller Base?). So TLJ is not doing anything different with Rey than Abrams did. Her journey remains the same. Huge raw power and no guidance and she is on a quest for guidance. And the explanation for her power was provided. And her parentage is not very different from Anakin’s. His mother was a slave and his father a mystery (or the force itself). Rey was sold by her parents for drinking money and they died in the Jakku desert. She is the force’s answer to Kylo Ren. The question is what is their purpose, she and Kylo. Their stories are entwined and both have a struggle, just not with the force.